Let \((G, \cdot )\)  be a group and \(S=S^{-1}\)  be a non empty subset of \(G\)  not containing the
identity element e of \(G\) . The Cayley graph \({\mathrm {Cay}}(G, S)\)  is the simple graph having vertex set \(G\)  and edge set
\(\lbrace \lbrace v, vs\rbrace  | v\in G, s \in S \rbrace \) . To find enough information about Cayley graphs, refer to
books Biggs [1]} and Godsil, Royle [2]}.
